General Relativity and Alternative Theories of Gravity

General Relativity (GR) is Einstein's geometric interpretation of the classical theory of gravity. It rests on the fundamental Einstein field equations, which relate the geometry of spacetime and the energy density of matter in a non-linear way. Accordingly, the gravitational force is equivalent to the curvature of spacetime. The gravitational interaction differs from all other interactions of the Standard Model, since the gravitational field (the metric), does not evolve on a given non-dynamical spacetime. Rather, it defines spacetime. Hence, the gravitational field interacts in a complicated manner with itself and the matter content.

On the one hand, experiments show that GR is a very accurate description of the gravitational field. Very important examples are the perihelion rotation of Mercury, the light deflection at the sun and gravitational lensing, black holes and particularly gravitational waves. Just recently, the LIGO collaboration was able to detect the gravitational wave signal stemming from the merging of two black holes. On the other hand, GR predicts its own breakdown. The celebrated Penrose-Hawking singularity theorems predict its own failure since the field equations become meaningless inside black holes and close to the Big Bang. Both, curvature and energy density, diverge. They become singular. This indicates that the theory has been pushed beyond the limits of validity and must be replaced by a more fundamental one.

There exist several candidate theories for such theories of quantum gravity, among which Loop Quantum Gravity (LQG).